Bloom Filters

Bloom filters are extremely space-efficient compared to hash tables, but at the cost of deterministic answers; that is, we get an answer that is unsure. It only guarantees that there won't be any false negatives, but there may be false positives. In other words, if we get a positive hit, the element may or may not be present; but if we get a negative, then the element is definitely not present.

Just like cuckoo hashing, we will use multiple hash functions here. However, we'll keep three functions, as two functions cannot achieve decent accuracy. The fundamental idea is that instead of storing the actual values, we store an array of Booleans indicating whether or not a value is (maybe) present.

To insert an element, we compute the value of all the hash functions and set the bits corresponding to all three hash values in the array to 1. For lookup, we compute the value of all the hash functions and check whether all the corresponding bits are set to 1. If so, we return...